Axial asymmetry in the IVBM

The dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U_{p}(3) \otimes \overline{U_{n}(3)} \supset SU^{\ast}(3) \supset SO(3)$, is considered and applied for the description of nuclear collective spectra exhibiting axially asymmetric features. The effect of the introduction of a Majorana interaction to the $SU^{\ast}(3)$ model Hamiltonian on the $\gamma$-band energies is studied. The theoretical predictions are compared with the experimental data for $^{192}Os$, $^{190}Os$, and $^{112}Ru$ isotopes. It is shown that by taking into account the full symplectic structures in the considered dynamical symmetry of the IVBM, the proper description of the energy spectra and the $\gamma$-band energy staggering of the nuclei under considerations can be achieved. The obtained results show that the potential energy surfaces for the following two nuclei $^{192}Os$ and $^{112}Ru$, possess almost $\gamma$-flat potentials with very shallow triaxial minima, suggesting a more complex and intermediate situation between $\gamma$-rigid and $\gamma$-unstable structures. Additionally, the absolute $B(E2)$ intraband transition probabilities between the states of the ground state band and $\gamma$ band, as well as the $B(M1)$ interband transition probabilities between the states of the ground and $\gamma$ bands for the two nuclei $^{192}Os$ and $^{190}Os$ are calculated and compared with experiment and for the $B(E2)$ values with the predictions of some other collective models incorporating the $\gamma$-rigid or $\gamma$-unstable structures. The obtained results agree well with the experimental data and reveal the relevance of the used dynamical symmetry of IVBM in the description of nuclei exhibiting axially asymmetric features in their spectra.Comment: 10 pages, 10 figures. arXiv admin note: text overlap with arXiv:1402.174

A Comparative Study of Some Pseudorandom Number Generators

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs, manufacturer installed routines and a random number sequence produced from physical noise. We start by traditional statistical tests, followed by detailed bit level and visual tests. The computational speed of various algorithms is also scrutinized. Our results allow direct comparisons between the properties of different generators, as well as an assessment of the efficiency of the various test methods. This information provides the best available criterion to choose the best possible generator for a given problem. However, in light of recent problems reported with some of these generators, we also discuss the importance of developing more refined physical tests to find possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables 2 and 7, and in the text, correspondingly

Boson-fermion mapping and dynamical supersymmetry in fermion models

We show that a dynamical supersymmetry can appear in a purely fermionic system. This ``supersymmetry without bosons" is constructed by application of a recently introduced boson-fermion Dyson mapping from a fermion space to a space comprised of collective bosons and ideal fermions. In some algebraic fermion models of nuclear structure, particular Hamiltonians may lead to collective spectra of even and odd nuclei that can be unified using the dynamical supersymmetry concept with Pauli correlations exactly taken into account.Comment: 20 pages. Revtex. One PostScript figure available on request from P

Partial Dynamical Symmetry in the Symplectic Shell Model

We present an example of a partial dynamical symmetry (PDS) in an interacting fermion system and demonstrate the close relationship of the associated Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding new light on this important interaction. Specifically, in the framework of the symplectic shell model of nuclei, we prove the existence of a family of fermionic Hamiltonians with partial SU(3) symmetry. We outline the construction process for the PDS eigenstates with good symmetry and give analytic expressions for the energies of these states and E2 transition strengths between them. Characteristics of both pure and mixed-symmetry PDS eigenstates are discussed and the resulting spectra and transition strengths are compared to those of real nuclei. The PDS concept is shown to be relevant to the description of prolate, oblate, as well as triaxially deformed nuclei. Similarities and differences between the fermion case and the previously established partial SU(3) symmetry in the Interacting Boson Model are considered.Comment: 9 figure

O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits with O(12) algebra which break F-spin but preserves the quantum number M_F. The generators of O(12) are derived and the quantum number `v' of O(12) for a given boson number N is determined by identifying the corresponding quasi-spin algebra. The O(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With the O(12) algebra identified, complete classification of pnIBM symmetry limits with good M_F is established.Comment: 22 pages, 1 figur

Parameter symmetries of quantum many-body systems

We analyze the occurrence of dynamically equivalent Hamiltonians in the parameter space of general many-body interactions for quantum systems, particularly those that conserve the total number of particles. As an illustration of the general framework, the appearance of parameter symmetries in the interacting boson model-1 and their absence in the Ginocchio SO(8) fermionic model are discussed.Comment: 8 pages, REVTeX, no figur